Contact:

Aims:

For two reasons, fast and accurate error estimation plays a key role in reliable and efficient
scientific computing: First, one may want to check whether the solution of a numerical simulation
is accurate enough. Second, if this is not the case, one aims to improve the discretization,
e.g., by local refinement of the underlying mesh.

Both subjects are usually covered by so-called a posteriori error estimates and related adaptive
mesh-refining algorithms. For error control in finite element methods (FEM), there is a broad
variety of a posteriori error estimators available, and convergence as well as optimality of
adaptive algorithms is well studied in the literature. This is in sharp contrast to the boundary
element method (BEM), where only few a posteriori error estimators have been proposed. Moreover,
even convergence of adaptive BEM is widely open. Finally, unlike the FEM, most a posteriori error
estimators for BEM are computationally expensive and even implementationally challenging.

The aim of the project is therefore threefold: First, to give a fair numerical comparison between
the error estimators and adaptive mesh-refining algorithms proposed in the BEM literature. Second,
to develop a posteriori error estimators in the context of BEM which are numerically cheap to
compute. Third, to study the convergence and the optimality of associated adaptive algorithms.